Hollande came under mounting pressure on Monday to clear up the confusion created by the latest developments in his complicated love life.
As the Socialist leader, who had pledged a "normal" presidency, came under increasing scrutiny at home and abroad for his alleged affair, attention in France has turned to the issue of whether his safety was compromised.
The apartment used by the couple was rented by a friend of Gayet's, another actress named Emmanuelle Hauck.
Hauck was the girlfriend of François Masini, who had reportedly had close links to the Corsican mafia and was shot dead on the island in May last year.
Before that she was married to actor Michel Ferracci, who has also been linked by the French media to the mafia. Ferracci got an 18-month suspended sentence in November for his role in money laundering.
"The head of the group in charge of security of the president, Sophie Hatt, was been rocked by the scandal and has to provide explanations to her superiors," Le Monde newspaper said on Monday.
It said the mafia links had escaped officials in charge of Hollande's security as well as the fact that the paparazzi had rented a flat in the area to photograph the movements of Hollande and Gayet.
The scandal broke over the weekend with a magazine, Closer, publishing photographs of Gayet, 41, arriving at the apartment building and others showing a helmeted man identified as Hollande also going there on a chauffeur-driven scooter.
Le Monde said Hollande was always accompanied by two policemen, who were personally chosen, during private visits and it was also the case during his trips to the borrowed apartment on the Rue du Cirque, near the presidential palace.
"But these police officers did not investigate the tenant's past and her links to nefarious individuals," it said.
They also failed to notice the photographers who were stalking Hollande and who had rented an apartment nearby to photograph him, it said.
The pensioner owner of the 'tryst' flat who rented to Hauck, meanwhile, denied media reports that the flat belonged to a mafioso or was used for sexual escapades.
I am profoundly shocked by all that is being said about me: that I am a former mafioso, the head of a (major) company or that the flat I lived in for 40 years was a brothel," Jean-Pierre Discazeaux, 71, told AFP.